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Set X consists of 100 bags of rice with an average weight of 90 pounds
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24 Jan 2023, 09:47
24 Jan 2023, 09:47
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Question Stats:
32% (02:40) correct
67% (02:10) wrong based on 28 sessions
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Set X consists of 100 bags of rice with an average weight of 90 pounds per bag, and the standard deviation of the weights is 8 pounds.
The weight of Bag A is 2 standard deviations below the average weight of the bags in set X. Bag B weighs 5 pounds more than the average weight of set X.
A. The quantity in Column A is greater.
B. The quantity in Column B is greater.
C. The two quantities are equal.
D. The relationship cannot be determined from the information given
The weight of Bag A is 2 standard deviations below the average weight of the bags in set X. Bag B weighs 5 pounds more than the average weight of set X.
Quantity A |
Quantity B |
Twice the difference between the weight of Bag B and the weight of Bag A |
The range of weights of the bags of rice in set X |
A. The quantity in Column A is greater.
B. The quantity in Column B is greater.
C. The two quantities are equal.
D. The relationship cannot be determined from the information given
Re: Set X consists of 100 bags of rice with an average weight of 90 pounds
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25 Jan 2023, 02:36
25 Jan 2023, 02:36
Expert Reply
OE
The information in the problem relates the weights of Bag A and Bag B to the average weight of the bags in the sample. Since Bag A is 2 standard deviations below normal weight, its weight is 90 - 2 x 8 = 74 pounds, and the difference between the weight of Bag B versus that of Bag A is (90 + 5) - 74 = 95 - 74 = 21 pounds. Thus, twice that difference is 42 pounds.
The range of the weight of the bags in set X could be less than, more than, or equal to 42. Dividing by the standard deviation, implies a range equivalent to 42/8= 5.25 standard deviations, which would be a large standardized range for a sample, but it's possible that the actual range is greater than that. Thus, the relationship cannot be determined from the information given.
The information in the problem relates the weights of Bag A and Bag B to the average weight of the bags in the sample. Since Bag A is 2 standard deviations below normal weight, its weight is 90 - 2 x 8 = 74 pounds, and the difference between the weight of Bag B versus that of Bag A is (90 + 5) - 74 = 95 - 74 = 21 pounds. Thus, twice that difference is 42 pounds.
The range of the weight of the bags in set X could be less than, more than, or equal to 42. Dividing by the standard deviation, implies a range equivalent to 42/8= 5.25 standard deviations, which would be a large standardized range for a sample, but it's possible that the actual range is greater than that. Thus, the relationship cannot be determined from the information given.
Re: Set X consists of 100 bags of rice with an average weight of 90 pounds
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19 Feb 2023, 22:50
19 Feb 2023, 22:50
Can anyone please explain what exactly do they mean "Dividing by the standard deviation, implies a range equivalent to 42/8= 5.25 standard deviations" - not making sense to me.
What am I missing here?
What am I missing here?
